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Implicit Differentiation

Evaluate the ...

Question

Evaluate the following integrals:
$2 x s i n (x^{2} + 1) d x$ , $x ϵ R$

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Solution

$2 x s i n (x^{2} + 1) d x$
Let $t = x^{2} + 1$ $\Rightarrow d t = 2 x d x$

$2 x s i n (x^{2} + 1) d x$ = $\int s i n t d t$ = $- c o s t + C$ = $- c o s (x^{2} + 1) + C$

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